Problem: Solve for $x$ : $3x - 3 = 7x + 6$
Solution: Subtract $3x$ from both sides: $(3x - 3) - 3x = (7x + 6) - 3x$ $-3 = 4x + 6$ Subtract $6$ from both sides: $-3 - 6 = (4x + 6) - 6$ $-9 = 4x$ Divide both sides by $4$ $\dfrac{-9}{4} = \dfrac{4x}{4}$ Simplify. $-\dfrac{9}{4} = x$